## Interpreting Linear and Exponential Functions Arising in Applications

On this page, due to explanation purposes, we will be learning mainly about LINEAR functions.

I have created a story for the purpose of explaining key features of the function, such as intercepts, intervals where the function is increasing, decreasing, positive, or negative; end behaviors.

Earrings Galore!

Gia is planning on making earrings for Christmas gifts. She is planning on making 2 pairs of earring per friend, and 5 pairs of earrings for her mother.

I have created a story for the purpose of explaining key features of the function, such as intercepts, intervals where the function is increasing, decreasing, positive, or negative; end behaviors.

Earrings Galore!

Gia is planning on making earrings for Christmas gifts. She is planning on making 2 pairs of earring per friend, and 5 pairs of earrings for her mother.

- Write the function that represents this scenario.

y=2x+5

- Describe the situation mathematically in context to the problem.

The problem states that Gia would like to make two earrings per friend. Because we do not know how many friends she is planning to make earrings for, we substitute the unknown number for

*x*. Therefore, the x variable represents the number of friends she will be making earrings for. Since she is making 2 earrings per

*x (friends)*, the 2 would be considered the slope if we were to graph this.

The problem also states that Gia wants to create five pairs of earrings for Mom. Since Mom is only one person, we do not need a variable for this part. We can add the number of earrings Gia is making for her mom at the end of the function. If we were to graph it, this would be the y-intercept.

Since the slope of this function would be positive two, the graph will always have a positive slope. The range will always increase as the domain increases. The number of friends is considered the domain, while the range is the number of earrings she will need.

- Graph the function.

Since we are comparing the graph to the situation, the graph has a point on o,5, instead of an arrow, because Gia can not make negative earrings. As you can see, the graphed line has a slope of positive 2, and is increasing at a constant rate. By plugging in any positive number, you will get a point on the line shown on the graph.

According to the graph, you can plug in any positive number and get an answer that is on the line, but since we are comparing it in context of the problem, we know that Gia can not make 9.987652189 earrings. Therefore, the domain can only consist of positive whole numbers.

According to the graph, you can plug in any positive number and get an answer that is on the line, but since we are comparing it in context of the problem, we know that Gia can not make 9.987652189 earrings. Therefore, the domain can only consist of positive whole numbers.